Rodgers has been on the lookout for defensive reinforcements for some time, though his search has stepped up a gear following an injury to summer signing Kolo Toure - who was stretchered off during the Capital One Cup tie with Notts County in mid-week.
Lescott's future at the Etihad remains unclear, with Manuel Pellegrini close to signing former charge Martin Demichelis for £3.5 million.
The Argentine played under Pellegrini during their time together at Malaga, and if his arrival is confirmed as expected, Lescott could be pushed further down the pecking order at the Etihad.
And although Lescott has started both of Manchester City's opening Premier League fixtures, the return of Matija Nastasic and Vincent Kompany from injury is likely to limit the 31-year-old's game time even further.
As well as Toure, Liverpool have also lost Sebastian Coates to injury, and with rumours still linking Reds duo Daniel Agger and Martin Skrtel with moves away from Anfield, Rodgers is keen to add to his depleted back line before the September 2 deadline.
According to reports, a bid of £7.5 million would be enough to tempt City into parting with the England international.